Research on methods of analytical ultracentrifugation is proposed. The areas of endeavor include: (1) Development of methods to determine point-by-point molecular weight averages in sedimentation velocity experiments. (2) Use of difference sedimentation velocity experiments to determine self-association and complex formation in impure protein mixtures. (3) Use of difference sedimentation equilibrium methods to determine stoichiometry and, perhaps, equilibrium constants of self- associating systems in impure mixtures. (4) Further study of the active enzyme sedimentation technique to determine molecular weights of active species and detection of minor active components. This methodology as well as established techniques are to be used to study the self-association of alpha-chymotrypsin at high pH, the mechanism of colchicine disruption of polymerized tubulin, and the self- associating IgG rheumatoid factors of rheumatoid arthritis. In addition to these projects it is proposed to digest dissociated enzymes with exopeptidases in order to create small, enzymatically active protein species. We propose to continue studies of the evolution of proteins of diverse structure and function. Computer methods are used to align the primary sequences of families of proteins. Work on the statistical evaluation of the alignment is proposed. Extension to assessment of 3 dimensional similarity is proposed. Bibliographic references: Pope, R.M., Mannik M., Gilliland, B.C., and Teller D.C: The Hyperviscosity Syndrome in Rheumatoid Arthritis due to Intermediate Complexes formed by Self-Association of IgG-Rheumatoid Factors. Arthritis and Rheumatism 18, 97-105 (1975); de Haen, C., Neurath, H., and Teller, D.C.: The Phylogeny of Trypsin-related Serine Proteases and Their Zymogens. New Methods for the Investigation of Distant Evolutionary Relationships. J. Mol. Biol. 92, 225-259 (1975).